Contravariant forms on Whittaker modules Brown, Adam Romanov, Anna Applied Mathematics General Mathematics Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell. American Mathematical Society 2021 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/8773 Brown A, Romanov A. Contravariant forms on Whittaker modules. <i>Proceedings of the American Mathematical Society</i>. 2021;149(1):37-52. doi:<a href="https://doi.org/10.1090/proc/15205">10.1090/proc/15205</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1090/proc/15205 info:eu-repo/semantics/altIdentifier/issn/0002-9939 info:eu-repo/semantics/altIdentifier/e-issn/1088-6826 info:eu-repo/semantics/altIdentifier/wos/000600416300004 info:eu-repo/semantics/altIdentifier/arxiv/1910.08286 info:eu-repo/semantics/openAccess